Abstract
The many-body localized (MBL) phase is characterized by a complete set of quasilocal integrals of motion and area-law entanglement of excited eigenstates. We study the effect of non-Abelian continuous symmetries on MBL, considering the case of symmetric disordered spin chains. The symmetry imposes strong constraints on the entanglement structure of the eigenstates, precluding conventional MBL. We construct a fixed-point Hamiltonian, which realizes a nonergodic (but non-MBL) phase characterized by eigenstates having logarithmic scaling of entanglement with the system size, as well as an incomplete set of quasilocal integrals of motion. We study the response of such a phase to local symmetric perturbations, finding that even weak perturbations induce multispin resonances. We conclude that the nonergodic phase is generally unstable and that symmetry implies thermalization. The approach introduced in this Rapid Communication can be used to study dynamics in disordered systems with non-Abelian symmetries, and provides a starting point for searching nonergodic phases beyond conventional MBL.
- Received 18 January 2017
DOI:https://doi.org/10.1103/PhysRevB.96.041122
©2017 American Physical Society